Symmetric equations in five variables with many solutions
Source: Germany 2024, Problem 1
June 14, 2024
system of equationsalgebraalgebra proposed
Problem Statement
The five real numbers satisfy the system of equations
\begin{align*}
v&=wx+ys,\\
v^2&=w^2x+y^2s,\\
v^3&=w^3x+y^3s.
\end{align*}
Show that at least two of them are equal.